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A240582 Largest absolute value of coefficient in the expression for the discriminant of a generic polynomial of degree n. 0

%I

%S 1,4,27,256,3750,77760,1728720,55494528,1948916016,146502720000,

%T 9131329626090

%N Largest absolute value of coefficient in the expression for the discriminant of a generic polynomial of degree n.

%D B. L. van der Waerden, Modern Algebra, Ungar, NY, Vol. I, 1953, pp. 82-83.

%e For n=3, f(x) = a x^3 + b x^2 + c x + d, discriminant = b^2 c^2 - 4 a c^3 - 4 b^3 d + 18 a b c d - 27 a^2 d^2. The largest absolute value of a coefficient is 27.

%p f := proc(n) local x,a,i; maxnorm(discrim(add(a[i]*x^i, i=0..n), x)) end: # _Roman Pearce_, Aug 29 2014

%t n = 6;

%t Table[List @@ Discriminant[Sum[a[j] x^j, {j, 0, i}], x] /. a[_] -> 1 //

%t Abs // Max, {i, n}]

%K nonn,more

%O 1,2

%A _Albert Lau_, Apr 08 2014

%E a(9)-a(11) from _Roman Pearce_, Aug 29 2014

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Last modified July 25 18:32 EDT 2021. Contains 346291 sequences. (Running on oeis4.)